First off, you'll have to make the hole bigger. Bigger? Yes, bigger. The hole needs to be uniform to create a proper patch, so using your keyhole saw or a utility knife, cut a square or rectangle around the hole to be patched.
Cut a piece of drywall 2" longer and 2" wider than the hole to be patched. Remember, always measure twice and cut once for accuracy. Lay the piece of drywall down on a flat surface, shiny side down. Measure in 1" from all four edges and, using your ruler, draw out the lines. The lines will form the exact shape and size of the hole. The idea is that the replacement piece will fit like a puzzle piece into the hole, with some paper extending beyond it to help bond it to the existing wall.
Using your ruler and utility knife, cut along the lines through the drywall to the bottom layer but do not cut the bottom layer of paper. This will be your patch. Using a putty knife, remove everything but the bottom layer of paper, making sure to keep the bottom layer intact.
Place the patch over the hole to measure it. The cut part should fit into the hole, and the paper should spread out an inch on each side. If not, go back to step 2 and try again, and remember, accuracy counts when measuring and cutting!
Put the patch down for now, and pick up your putty knife. Spread a little spackling compound around the hole—not much, just enough to coat the surface. Place the patch back into the hole, then smooth the outer edge of the patch down onto the compound. Spread a small amount of compound over the edges, feathering the edges as you smooth it out. Allow it to dry, following the drying times on your compound. Short on time? Aim a hairdryer at the spot on low heat to speed up drying time. Not too hot, though, or the drywall and paint surrounding the hole will crack.
When it's completely cured, sand it lightly until the patch is flush with the wall. If your wall is textured, apply more mud and smooth it with a putty knife or even with your fingers until the texture appears even. If it's an "orange peel" texture, you might consider purchasing a can of sprayable texture. Just point the can at the affected area, spray, dry, sand if necessary, prime and paint.
The toughest part of patching a hole is getting the paint to match, so hopefully you have some of color left over from your original paint job. (This is reason to always save a little excess paint.) Apply a thin layer of primer first, and feather the edges so they blend into the rest of the paint job. When primer is completely dry, apply paint lightly, feathering the edges to blend it in. Don't judge your work until the paint has time to cure. Once it's dry if you find you've been a bit heavy-handed, re-sand, re-prime and hit the paintbrush again. Too light? Paint on another coat!
There's no need to let your walls look like Swiss cheese. Learn how to fix life's little mistakes because it's just a matter of time before someone pokes a hole in your house. Being able to smooth things over also means you'll be less wary about hanging new prints or putting up shelving. It's your house and you can have it your way!